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- W4287687620 abstract "In this paper we discuss the relationship between direct products of monounary algebras and their components, with respect to the properties of residual finiteness, strong/weak subalgebra separability, and complete separability. For each of these properties $mathcal{P}$, we give a graphical criterion $mathcal{C_P}$ such that a monounary algebra $A$ has property $mathcal{P}$ if and only if it satisfies $mathcal{C_P}$. We also show that for a direct product $Atimes B$ of monounary algebras, $Atimes B$ has property $mathcal{P}$ if and only if one of the following is true: either both $A$ and $B$ have property $mathcal{P}$, or at least one of $A$ or $B$ are backwards-bounded, a special property which dominates direct products and which guarantees all $mathcal{P}$ hold." @default.
- W4287687620 created "2022-07-26" @default.
- W4287687620 creator A5074897740 @default.
- W4287687620 date "2020-08-18" @default.
- W4287687620 modified "2023-09-26" @default.
- W4287687620 title "Residual Finiteness and Related Properties in Monounary Algebras and their Direct Products" @default.
- W4287687620 doi "https://doi.org/10.48550/arxiv.2008.07943" @default.
- W4287687620 hasPublicationYear "2020" @default.
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